22-Agric-B5 Power Units for Agricultural, Biosystems, and Food Industries · May 2015
Question 4 of 4: Usable Tractor Engine Power After Derating
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
National Exams — May 2015 — 04-Agric-B5, Power Units for Agricultural, Biosystems and Food Industries. Three-hour, open-book exam; any non-communicating calculator is permitted. Format: four questions constitute a complete paper, each of equal value; all questions require calculation.
Reference texts: Srivastava, Buckmaster & Hull, Engineering Principles of Agricultural Machines (2nd ed., ASABE) — sprocket/pulley speed ratios, indicated engine power, piston displacement and compression ratio; Kepner, Bainer & Barger, Principles of Farm Machinery (3rd ed.) — PTO power trains and tractor engine derating; OSHA 29 CFR 1910.95, Occupational Noise Exposure — noise-dose formula (5 dB exchange rate, as printed on this paper).
Problem 4: Usable Tractor Engine Power After Derating (equal value)
Given. Basic engine rating $P_{\text{basic}}=75$ hp; derating $10\%$ for accessories and $5\%$ for the cooling fan, each expressed as a fraction of the basic rating.
Find. The usable (net) power delivered after both derating losses.
Figure 4 — power-derating cascade: each loss is a stated percentage of the ORIGINAL basic rating (7.5 hp and 3.75 hp), subtracted in sequence to leave the usable power.
Approach. Treat each stated percentage as a fraction of the basic (gross) rating and subtract both losses from it.
Accessory and fan losses.
$$\Delta P_{\text{acc}} = 0.10(75) = 7.5\ \text{hp} \qquad \Delta P_{\text{fan}} = 0.05(75) = 3.75\ \text{hp}$$
Usable power.
$$P_{\text{usable}} = P_{\text{basic}} - \Delta P_{\text{acc}} - \Delta P_{\text{fan}} = 75 - 7.5 - 3.75 = \boxed{63.75\ \text{hp}}$$
Discussion: nearly 15% of the basic engine rating (11.25 hp) is consumed just running the engine's own accessories and cooling fan before any of the power reaches the drawbar or PTO — this is why published "PTO horsepower" or "drawbar horsepower" ratings always run below the engine's own gross/basic rating.
Quantity
Result
Accessory loss
7.5 hp
Fan loss
3.75 hp
Usable power
63.75 hp
Check: assumes both derating percentages are fractions of the ORIGINAL basic rating, summed then subtracted (additive derating, $P_{\text{usable}}=P_{\text{basic}}(1-0.10-0.05)=63.75$ hp) — the standard convention for published tractor-test derating tables (Kepner, Bainer & Barger), where each accessory's loss is quoted as a percentage of the gross rating. An alternative successive/multiplicative reading ($75\times0.90\times0.95=64.125$ hp, treating the fan loss as 5% of the ALREADY-reduced power) would give a usable power about 0.6% higher; the question's wording ("derating 10% ... and 5% ...", both stated against the single basic rating) supports the additive reading used here.
